A continuum-based reaction-diffusion model for spread of gene silencing in chromosomal inactivation

Regulation of gene silencing in large chromosomal regions is crucial for development and disease progression. One example of massive gene silencing is X chromosome inactivation (XCI), a process essential for gene dosage compensation. During XCI, most genes in the chromosome are inactivated following the transcription of long noncoding RNA XIST. Recent experiments showed that the spread of silencing is restricted in space but the mechanism of controlling the spread remains unclear. Here, we develop a continuum-based, reaction-diffusion model that elucidates chromosomal inactivation through a regulatory network for XIST-mediated gene silencing. We find that the spread of XIST can be tuned by known negative feedback loops regulating its synthesis and degradation, and that the spread of gene silencing is controlled by a wave-pinning mechanism driven by global regulation of silencing complex together with local epigenetic regulators. We use a 3D chromosome structure inferred from experimental data and our modeling framework to show the spatiotemporal regulation for spread of gene silencing. Our method enables the investigation for the inactivation dynamics of large regions of chromosomes with varying degrees of the spread of gene silencing. Our model provides mechanistic insights that quantitatively relate gene regulatory networks to tunability and stability of chromosomal inactivation.